Precalculus Functions and Graphs (with CD-ROM, Make the Grade, and InfoTrac)

Precalculus : Functions and Graphs

Precalculus Functions and Graphs (with CD-ROM)

Precalculus Functions and Graphs

Summary

This latest edition in the highly respected Swokowski/Cole precalculus series retains the elements that have made it so popular with instructors and students alike: its exposition is clear, the time-tested exercise sets feature a variety of applications, its uncluttered layout is appealing, and the difficulty level of problems is appropriate and consistent. Mathematically sound, PRECALCULUS: FUNCTIONS AND GRAPHS, Tenth Edition, effectively prepares students for further courses in mathematics through its excellent, time-tested problem sets. This edition has been improved in many respects including the addition of technology inserts with specific keystrokes for the TI-83 Plus and the TI-86, ideal for students who are working with a calculator for the first time. The design of the text makes the technology inserts easily identifiable, so if a professor prefers to skip these sections it is simple to do so.

Table of Contents

List of Graphing Calculator Topics

x

Preface

xii

Topics from Algebra

1

(92)

Real Numbers

2

(17)

Exponents and Radicals

19

(12)

Algebraic Expressions

31

(17)

Equations

48

(19)

Complex Numbers

67

(8)

Inequalities

75

(18)

Chapter 1 Review Exercises

87

(3)

Chapter 1 Discussion Exercises

90

(3)

Graphs and Functions

93

(114)

Rectangular Coordinate Systems

94

(9)

Graphs of Equations

103

(16)

Lines

119

(19)

Definition of Function

138

(18)

Graphs of Functions

156

(17)

Quadratic Functions

173

(16)

Operations on Functions

189

(18)

Chapter 2 Review Exercises

199

(6)

Chapter 2 Discussion Exercises

205

(2)

Polynomial and Rational Functions

207

(72)

Polynomial Functions of Degree Greater Than 2

208

(11)

Properties of Division

219

(8)

Zeros of Polynomials

227

(14)

Complex and Rational Zeros of Polynomials

241

(8)

Rational Functions

249

(18)

Variation

267

(12)

Chapter 3 Review Exercises

275

(2)

Chapter 3 Discussion Exercises

277

(2)

Inverse, Exponential, and Logarithmic Functions

279

(80)

Inverse Functions

280

(11)

Exponential Functions

291

(13)

The Natural Exponential Function

304

(11)

Logarithmic Functions

315

(15)

Properties of Logarithms

330

(8)

Exponential and Logarithmic Equations

338

(21)

Chapter 4 Review Exercises

352

(3)

Chapter 4 Discussion Exercises

355

(4)

The Trigonometric Functions

359

(102)

Angles

360

(11)

Trigonometric Functions of Angles

371

(18)

Trigonometric Functions of Real Numbers

389

(19)

Values of the Trigonometric Functions

408

(8)

Trigonometric Graphs

416

(15)

Additional Trigonometric Graphs

431

(8)

Applied Problems

439

(22)

Chapter 5 Review Exercises

452

(7)

Chapter 5 Discussion Exercises

459

(2)

Analytic Trigonometry

461

(68)

Verifying Trigonometric Identities

462

(6)

Trigonometric Equations

468

(15)

The Addition and Subtraction Formulas

483

(11)

Multiple-Angle Formulas

494

(10)

Product-to-Sum and Sum-to-Product Formulas

504

(5)

The Inverse Trigonometric Functions

509

(20)

Chapter 6 Review Exercises

525

(3)

Chapter 6 Discussion Exercises

528

(1)

Applications of Trigonometry

529

(66)

The Law of Sines

530

(10)

The Law of Cosines

540

(9)

Vectors

549

(16)

The Dot Product

565

(11)

Trigonometric Form for Complex Numbers

576

(7)

De Moivre's Theorem and nth Roots of Complex Numbers

583

(12)

Chapter 7 Review Exercises

589

(4)

Chapter 7 Discussion Exercises

593

(2)

Systems of Equations and Inequalities

595

(96)

Systems of Equations

596

(10)

Systems of Linear Equations in Two Variables

606

(8)

Systems of Inequalities

614

(10)

Linear Programming

624

(8)

Systems of Linear Equations in More Than Two Variables

632

(16)

The Algebra of Matrices

648

(10)

The Inverse of a Matrix

658

(6)

Determinants

664

(7)

Properties of Determinants

671

(8)

Partial Fractions

679

(12)

Chapter 8 Review Exercises

685

(3)

Chapter 8 Discussion Exercises

688

(3)

Sequences, Series, and Probability

691

(84)

Infinite Sequences and Summation Notation

692

(16)

Arithmetic Sequences

708

(7)

Geometric Sequences

715

(9)

Mathematical Induction

724

(7)

The Binomial Theorem

731

(9)

Permutations

740

(7)

Distinguishable Permutations and Combinations

747

(9)

Probability

756

(19)

Chapter 9 Review Exercises

770

(3)

Chapter 9 Discussion Exercises

773

(2)

Topics from Analytic Geometry

775

(80)

Parabolas

776

(10)

Ellipses

786

(14)

Hyperbolas

800

(12)

Plane Curves and Parametric Equations

812

(15)

Polar Coordinates

827

(17)

Polar Equations of Conies

844

(11)

Chapter 10 Review Exercises

850

(2)

Chapter 10 Discussion Exercises

852

(3)

Appendixes

855

I Common Graphs and Their Equations

856

(2)

II A Summary of Graph Transformations

858

(2)

III Graphs of Trigonometric Functions and Their Inverses

860

(2)

IV Values of the Trigonometric Functions of Special Angles on a Unit Circle